Theorem 1 (The main theorem of the formal calculus of variations,
see, for example, [1]}, and the references therein) 
The linear spaces
\(H^q_\mathrm {H}(\mathbf {B})={\left\lbrace \begin{array}{ll}0, & q<0, q>m ;\\\mathbb {R}, & q=0 ; \\0, & 1\le q\le m-1 ; \\{\cal H}(\mathbf {B}), & q=m;\end{array}\right.}\) 
